Proving irrationality

1. Oct 30, 2008

hew

1. The problem statement, all variables and given/known data

decide if sqrt2 + sqrt5 +sqrt7 is rational or irrational, with proof

2. Relevant equations

3. The attempt at a solution
i assumed that it was rational, the equation =r
sqrt2 + sqrt 5=r- sqrt7
7 + 2sqrt10=r^2 + 7 -2r*sqrt7
2sqrt10=r^2 -2r*sqrt7
could i have a hint on how to rearrange this, i have already proved in an earlier question that sqrt2, sqrt5, sqrt7 are irrational

thankyou

2. Oct 30, 2008

Office_Shredder

Staff Emeritus
You're almost there. square both sides again, and you can write sqrt(7) as a linear combination of rational numbers. i.e. you've shown sqrt(7) is rational.